DARK MATTER, DARK ENERGY, AND ALTERNATE MODELS: A REVIEW Kenath Arun*1,2, S B Gudennavar and C Sivaram3 1 2
Department of Physics, Christ University, Bengaluru-560029, Karnataka, India
Department of Physics, Christ Junior College, Bengaluru-560029, Karnataka, India 3
Indian Institute of Astrophysics, Bengaluru-560034, Karnataka, India
Abstract: The nature of dark matter (DM) and dark energy (DE) which is supposed to constitute about 95% of the energy density of the universe is still a mystery. There is no shortage of ideas regarding the nature of both. While some candidates for DM are clearly ruled out, there is still a plethora of viable particles that fit the bill. In the context of DE, while current observations favour a cosmological constant picture, there are other competing models that are equally likely. This paper reviews the different possible candidates for DM including exotic candidates and their possible detection. This review also covers the different models for DE and the possibility of unified models for DM and DE. Keeping in mind the negative results in some of the ongoing DM detection experiments, here we also review the possible alternatives to both DM and DE (such as MOND and modifications of general relativity) and possible means of observationally distinguishing between the alternatives. Keywords: Dark matter; dark energy; WIMPs; axions; Mirror Dark Matter; cosmological constant; Quintessence; Chaplygin Gas; Dieterici Gas; MOND; modifications of general relativity
*
Corresponding author: e-mail:
[email protected] Telephone: +91-80-4012 9292; Fax: +91-80- 4012 9222
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1. Introduction 2. Dark Matter 2.1 Observational Evidence for Dark Matter 2.2 Classification of Dark Matter 2.2.1
Decaying Dark Matter
2.3 What Dark Matter Cannot Be 2.3.1
Massive Astrophysical Compact Halo Object
2.3.2
Hot Dark Matter and Neutrinos
2.3.3
Other Proposed Candidates
2.4 Possible Candidates of Dark Matter 2.4.1
Weakly Interacting Massive Particles
2.4.2
Axions
2.4.3
Primordial Black Holes
2.4.4
Exotic Candidates
2.4.4.1 Fermi Balls 2.4.4.2 Nuclear Balls 2.4.4.3 EW Balls and GUT Balls 2.4.5
New Class of Dark Matter Objects
2.4.6
Mirror Dark Matter
2.5 Detection of Dark Matter 2.5.1
Direct Detection Experiments
2.5.2
Indirect Detection Experiments
3. Dark Energy 3.1 Cosmological Constant 3.2 Quintessence 3.3 Phantom Energy 3.4 Quintom Dark Energy 3.5 Dark Energy and Mach’s Principle 3.6 Gurzadyan – Xue Dark Energy 4. Dark Matter and Dark Energy 4.1 Change in Equation of State 2
4.1.1
Chaplygin Gas
4.1.2
Dieterici Gas
4.1.3
Long Range DM particle Interactions
4.1.4
Viscous Dark Matter
5. Alternate Models to Dark Matter and Dark Energy 5.1 Modification of Newtonian Dynamics and Modification of Newtonian Gravity 5.2 Tensor–Vector–Scalar Theory 5.3 Modification of Einstein-Hilbert Action 5.4 Can MOND be differentiated from Newtonian DM Theory? 5.5 Dark Energy and Modified Gravity 6. Summary and Outlook References
1. Introduction One of the most unexpected revelations about our understanding of the universe is that the universe is not dominated by the ordinary baryonic matter, but instead, by a form of nonluminous matter, called the dark matter (DM), and is about five times more abundant than baryonic matter (Ade et al., 2014). While DM was initially controversial, it is now a widely accepted part of standard cosmology due to observations of the anisotropies in the cosmic microwave background, galaxy cluster velocity dispersions, large-scale structure distributions, gravitational lensing studies, and X-ray measurements from galaxy clusters. Another unresolved problem in cosmology is that the detailed measurements of the mass density of the universe revealed a value that was 30% that of the critical density. Since the universe is very nearly spatially flat, as is indicated by measurements of the cosmic microwave background, about 70% of the energy density of the universe was left unaccounted for. This mystery now appears to be connected to the observation of the non-linear accelerated expansion of the universe deduced from independent measurements of Type Ia supernovae (Riess et al., 1998; Perlmutter et al., 1999; Peebles and Ratra, 2003; Sivaram, 2009). Generally one would expect the rate of expansion to slow down, as once the universe started expanding, the combined gravity of all its constituents should pull it back, i.e. decelerate it (like a stone thrown upwards). So the deceleration parameter (q 0 ) was expected to be a 3
positive value. A negative q 0 would imply an accelerating universe, with repulsive gravity and negative pressure. And the measurements of Type Ia supernovae have revealed just that. This accelerated expansion is attributed to the so-called dark energy (DE). There are several experiments to detect postulated DM particles running for many years that have yielded no positive results so far. Only lower and lower limits for their masses are set with these experiments so far. The motto seems to be ‘absence of evidence is not evidence of absence’. But if future experiments still do not give any clue about the existence of DM, one may have to consider looking forward for alternate theories (Sivaram, 1994a; 1999). The best example of this is that of the orbit and position of Vulcan, which was theoretically inferred from the observation of Mercury orbit (Hsu and Fine, 2005). The deviation of its orbit, as predicted by Newtonian gravity, was attributed to the missing planet (DM). But the resolution of this discrepancy came through the modification of Newtonian gravity by Einstein and not by DM. This is unlike in the case of Uranus were the prediction and discovery were successful using DM (Neptune) theory (Kollerstrom, 2001).
2. Dark Matter 2.1 Observational Evidence for Dark Matter The evidence for the existence of such non-radiating matter goes back to more than eighty years ago, when Zwicky (1937) was trying to estimate the masses of large clusters of galaxies. Surprisingly it was found that the dynamical mass of the cluster, deduced from the motion of the galaxies (i.e. their dispersion of velocities), in a large cluster of galaxies were at least a hundred times their luminous mass. This led Zwicky to conclude that most of the matter in such clusters is not made up of luminous objects like stars, or clusters of stars, but consists of matter which does not radiate (Zwicky, 1937). Zwicky’s observations were later confirmed by others and although he had overestimated the amount of DM it is now accepted as an established paradigm. Later observations starting about forty years ago, and continuing till now also revealed unmistakably that even individual galaxies like our Milky Way are dominated by DM (Rubin and Ford, 1970; Rubin, Ford and Thonnard, 1980). We know this for galaxies because it turns out that objects orbiting the galaxy at larger distances from the galactic centre move around more or less the same velocity as objects much closer to the centre, contrary to what is expected (Jones and Lambourne, 2004). 4
The rotational velocity should drop as v c µ r -1 2 , like in solar system. But at large distances, rotational curve becomes flat, i.e. v c ª constant. This is valid for all spherically symmetric system and is valid at large distances. This gives information that mass is still growing even after light dies out ( M µ R ). Indeed, as much as 90% of the galaxy mass is due to DM. This can only be accounted for if the mass progressively increases with radius as we move out further and further away from the central region. But this matter does not radiate as most of the light is from the central region. So the conclusion is that 90% of the galaxy is DM. This seems to be universally true for all types of galaxies. Even in dwarf galaxies, the motion of their stars indicates the presence of DM (Bell and de Jong, 2001; Stierwalt et al, 2017). Even the ‘missing satellite problem’ (Moore et al., 1999; Nierenberg et al., 2016), which arises from numerical cosmological simulations that predict the evolution of the distribution of matter in the universe, could be attributed to the fact that many dwarfs have a huge amount of dark matter but very few stars, making them difficult to detect due to their inherent faintness. Cosmological models predict that a halo the size of our Galaxy should have about 50 dark matter satellites with circular velocity greater than 20kms-1 and mass greater than 300 million solar mass within a 570kpc radius. But the actual number of observed satellites is much lesser. The difference is even larger in the case of galaxy groups like the Local Group. (Klypin et al., 1999) Recently, Beasley et al. (2016) reported measurements of ultra diffuse galaxies (UDGs) which have the sizes of giants but the luminosities of dwarfs. Deep imaging surveys of Fornax, Virgo, Coma and the Pisces-Perseus superclusters have revealed substantial populations of faint systems that were hidden from earlier surveys. Coma cluster for instance consists of galaxies with sizes similar to that of the Milky Way, but stellar luminosities similar to that of dwarfs. Measurements from a UDG (VCC 1287 in the Virgo cluster), based on its globular cluster system dynamics and size indicates a virial mass of ~ 8 ¥ 1010 solar mass, yielding a dark matter to stellar mass fraction of ~3000 indicating that about 99.96% of the galaxy is dark matter (Beasley et al., 2016). Apart from velocity distribution of galaxies and galaxy clusters, there are other evidences pointing to the presence of dark matter. Extended emission in X-ray observations of clusters of galaxies indicates presence of hot gas distributed throughout the cluster volume (Ferrari, 2008). If the gas is in virial equilibrium within the cluster we have: 5
kT ~
1 mp v2 2
... (2.1)
where the thermal velocity is ~1000kms-1. This implies a temperature of T ~ 6 ¥ 10 7 K , which produces bremsstrahlung emission in X-rays. The total emission power density, integrated over all frequencies is given by:
e ff
1.4 ¥ 10 -27 Z 2 ne ni T
1
2
... (2.2)
Where, n e , ni are the number density of electrons and ions respectively, Z is the atomic number and T is the temperature. From X-ray observations, luminosity can be measured, which depends on density, temperature and volume of the cluster. The mass required to hold hot gas in cluster estimated requires vast amount of DM. Hot gas itself accounts for ~20% mass in rich clusters (which is several times mass of star). Results from Chandra X-ray Observatory on the distribution of dark matter in a massive cluster of galaxies (such as Abell 2029, which consists of thousands of galaxies surrounded by a huge cloud of hot gas) indicate that the cluster is primarily held together by the gravity of the dark matter (Vikhlinin et al., 2006; Dietrich et al., 2012). Another method to detect the presence of DM is gravitational lensing. This method provides for an alternate method of measuring the mass of the cluster without relying on observations of dynamics of the cluster (Tyson, Valdes and Wenk, 1990). All these different methods point to the currently accepted scenario that ~80% of the total amount of matter in the galaxy is a form of DM. An important argument in favour of the existence of DM is the growth of structures. Observations suggest a bottom-up scenario, with the smallest structures collapsing first, followed by galaxies and then galaxy clusters. Cosmic Microwave Background (CMB) anisotropy measurements indicate models with predominant DM. DM hypothesis also agrees with statistical surveys of the visible structure. The gravity from DM increases the compaction force, allowing the formation of structures. Simulations of billions of dark matter particles seem to confirm that a DM model of structure formation is consistent with the structures observed through galaxy surveys, such as the
6
Sloan Digital Sky Survey and 2dF Galaxy Redshift Survey, as well as observations of the Lyman-alpha forest (Springel et al., 2005; Gao et al., 2005).
2.2 Classification of Dark Matter An important categorization scheme for DM particles is the ‘hot’ vs. ‘cold’ classification. Hot Dark Matter (HDM) particles are those that are described by a relativistic equation of state at the time when galaxies could just start to form. And Cold Dark Matter (CDM) particles are those described by non-relativistic equation of state at the time when galaxies could just start to form. Some weakly interacting particles (like WIMPs), Supersymmetric, superstring, higher dimensions, Kaluza Klein etc. could be CDM, forming sub galactic objects first (i.e. bottom-up scenario) (Gelmini, 2006; Cheng, Chu and Tang, 2015). This categorization has important ramifications for structure formation, and there is a chance of determining whether the dark matter is hot or cold from studies of galaxy formation. Hot dark matter cannot cluster on galaxy scales until it has cooled to non-relativistic speeds, and so gives rise to a different primordial fluctuation spectrum (Davis et al., 1985). Warm dark matter (WDM) is another hypothesized form of dark matter that has properties intermediate between those of HDM and CDM, causing structure formation to occur bottom-up from above their free-streaming scale, and top-down below their free streaming scale. The most common WDM candidates are sterile neutrinos and gravitinos. WDM particles interact much more weakly than neutrinos. They decouple at temperatures much greater than the QCD temperature, and are not heated by the subsequent annihilation of hadronic species. Consequently their number density is roughly an order of magnitude lower, and their mass an order of magnitude higher, than HDM particles (Silk, 2000). The cut-off in the power spectrum implied by WDM will inhibit the formation of small DM halos at high redshift. But such small halos are where the first stars form, which produce metals uniformly throughout the early universe as indicated by observations of the Lyman alpha forest. Thus from observations the current favourite model for the universe is where the matter is mostly CDM (with a large cosmological constant, i.e. LCDM).
2.2.1 Decaying Dark Matter Dark matter has survived until the present day, accounting for ~26% of the present energy density of the universe. It is still unknown whether these DM particles are absolutely 7
stable or they have a finite but very long lifetime. This is a possibility since there is no theoretical basis predicting their stability. In most models, dark matter stability is imposed ad hoc by imposing extra symmetries. Many particle physics models exist which contain unstable (very long-lived) DM particles. It is conceivable that the dark matter stability could be due to symmetry of the renormalisable part of the Lagrangian which is broken by higher dimensional operators, which could thus induce the dark matter decay (Bertone, Hooper and Silk, 2005). Emission line-like spectral feature at energy E ~3.5 keV in the long exposure X-ray observations of a number of dark matter-dominated objects, such as the stack of 73 galaxy clusters (Bulbul et al., 2014) and in the Andromeda galaxy and the Perseus galaxy cluster (Boyarsky et al., 2014) has recently been observed. The possibility that this spectral feature may be the signal from decaying DM has sparked a lot of interest, and many dark matter models explaining this signal have been proposed.
2.3 What Dark Matter Cannot Be 2.3.1 Massive Astrophysical Compact Halo Object The observed abundance of light elements created during the primordial nucleosynthesis can rule out the possibility that DM particles are baryonic in nature. The primordial nucleosynthesis strongly depends on the baryon-photon ratio. This is also supported by the observations of cosmic microwave background radiation. The main baryonic candidates are the Massive Astrophysical Compact Halo Object (MACHO) class of candidates. These include brown dwarf stars, Jupiter-like planets, and 100 solar mass black holes. Brown dwarfs are spheres of H and He with masses below 0.08 solar mass, so they never begin nuclear fusion of hydrogen. The MACHO project which analysed microlensing events from the Large Magellanic Cloud indicates that such objects can account for only about 10 – 20% of the missing DM (MACHO Collaboration, Alcock et al., 2000). Another group, the EROS-2 collaboration does not confirm the signal claims by the MACHO group. They did not find enough microlensing effect with sensitivity higher by a factor of 2 (Tisserand et al., 2007). These searches have ruled out the possibility that these objects make up a significant fraction of dark matter in our galaxy. 8
2.3.2 Hot Dark Matter and Neutrinos The formation of such large scale structures raises few questions, including the very existence of large scale structures in just a few billion years, from a smooth homogeneous (uniform density) expanding universe and which objects formed first (top-down or bottom-up process). Early analysis due to Jeans (1902) (much before discovery of Hubble), gives the balance between dissipative pressure force and attractive gravity in a medium of pressure P and density
r , i.e. PdV
Gravitational energy. This implies that there is a minimal size R, for structures to
grow under its own gravity, which is given by: R≥
c sound Gr
~
(rR
gas
T)
(Gr )
1
1
2
... (2.3)
2
In an expanding medium, where r µ t -2 , like the Friedmann-Robertson-Walker (FRW) universe, growth rate is not exponential, but follows power law. Any inhomogeneity in density, characterized as
r - r av r av
dr r
d , grows under gravity with time, where r av is the average
density. The inhomogeneity described by d , are believed to have formed very early, during the inflation era. The primordial fluctuations (of scalar field) were already imprinted on it. In expanding universe any gravitational contraction has to counteract expansion of ambient medium and pressures (also dark energy), with d >> 1 at end of structure formation process. In the beginning d Rmin , it reduces to the usual GR. In the expansion, i.e. f ( R)
R + a ' Rm in + b
Rm2 in + ... , the first term represents GR, the R
second term is a background minimal curvature, equivalent to L , which shows the presence of DE. The higher order terms involving R m2 in are too small to significantly contribute to the local behaviour, so with the first two terms it may be difficult to distinguish this theory from GR with a cosmological constant. There are 1
R
theories that have been suggested, which do not require DE but have
accelerating universe. These alternative gravity theories that do not require some unknown DE or DM should satisfy all tests of GR as well as match with observations. There are problems with galaxy formation in MOND (Sivaram 1994a). These theories also have severe constraints from CMB anisotropy and lensing. So far there are no complete theories, although string theory could give scalar tensor theories in low energy limit. In general, these models are equivalent to GR plus massive scalar fields. Solar System tests for relativistic theories of gravity include gravitational redshift, deflection of light by the Sun, and planetary orbit precession at perihelion and GR is consistent with these experimental tests. Any correction to the Newtonian potential has to satisfy the constraints on equivalence principle and solar system observations. Also, the new gravitationally-induced interactions lead to observable effects at microscopic and macroscopic scales. These facts make very unlikely the viability of f (R ) models in accounting for the change in the late cosmic evolution (Olmo, 2007), apart from difficulties with equivalence principle, as f (R ) theories are necessarily equivalent to scalartensor theories (Sivaram and Campanelli, 1992a; 1992b). Gravitational wave astronomy, starting with the event GW150914 (LIGO Scientific Collaboration and Virgo Collaboration, Abbott et al., 2016), could be fundamental for discriminating various theories of gravity. With improved sensitivity and advanced detection of gravitational waves, then the accurate angle- and frequency-dependent response functions of 40
interferometers for gravitational waves arising from various theories of gravity, i.e. general relativity and extended theories of gravity will be the definitive test for general relativity, and help in discriminating among various gravity theories (Corda, 2009).
5.4 Can MOND be differentiated from Newtonian DM Theory? As seen above, two poplar theoretical concepts to resolve the apparent inconsistency of Newtonian dynamics over galactic scales and beyond is assumption of ubiquitous presence of DM and secondly the assumption that Newtonian gravitational law or dynamics requires modification. Dunkel (2004) argues that for a system satisfying a fixed relationship between gravitational fields caused by DM and visible matter, a generalised MOND equation reducing to the usual MOND law can be formulated. Thus MOND is interpreted as a special case of DM theory. Briefly both gravitational potentials f v ( x ), f d ( x ) due to visible and DM satisfying Poisson equations, — 2f (v, d ) 4pGr (v, d ) , for both visible and DM leading to the equations of motion: m&x&
-m—[fv (x ) + f d (x )]
... (5.27)
Defining the accelerations g (v, d )(x ) -—f (v, d )x , this is written as, &x&
g (v ) + g (d )
g , and if
further assumed that these acceleration vectors point in the same direction:
With g v
Ê g (d ) ˆ &x& ÁÁ1 + ˜g v g (v ) ˜¯ Ë
... (5.28)
Ê ˆ Á ˜ 1 &x& Á1 + ˜gv g Á -1˜ gd Ë ¯
... (5.29)
g - g d ≥ 0 , we have:
gv
Ê e ˆ Á ˜g Ë e + 1¯
m (e )g , e ( x )
g (x ) -1 ≥ 0 g d (x )
... (5.30)
So we have a generalisation of the MOND equation,
gv
Ê gˆ m ÁÁ ˜˜ g Ë a0 ¯
41
... (5.31)
Here, instead of the constant a 0 of MOND, we have the acceleration field a( x ) defined as,
e (x )
g (x ) a(x )
1 a(x )
1
g d (x )
g (x ) -1 g d (x )
-
... (5.32)
1 , g (x ) g (x )
g v (x ) + g d (x )
... (5.33)
MOND is the special case where a( x ) a 0 , which implies a fixed relation between acceleration fields due to visible and DM. It can be seen from the above relation that for a 0 to be small, galaxies satisfying MOND limit are DM dominated. (Again e (r ) Æ 0 , as g (r ) Æ g d (r ) , i.e. DM dominated, the Tully-Fisher law also follows.) Current Ê a• > 0 Á a• Ë
DM
models
cannot
explain
in
which
cases
g v
